Conventional magnetic storage devices include a magnetic transducer or "head" suspended in close proximity to a recording medium, for example, a magnetic disk having a plurality of concentric tracks. The transducer is supported by an air-bearing slider mounted to a flexible suspension. The suspension in turn is attached to a positioning actuator. During normal operation, relative motion is provided between the head and the recording medium as the positioning actuator dynamically positions the head over the desired track. The information recorded on the magnetic disk is transmitted to a preamplifier which is in turn transmitted to a read channel. One example of read channels in use in today's technology is a PRML read channel.
The magnetic recording channel can be characterized as a channel with significant intersymbol interference, particularly at high recording densities. Partial response maximum likelihood (PRML) detection systems based on shaping the channel response to a suitable partial response have become a popular detection method for such channels. Partial responses such as class IV partial response (PR4) and enhanced PR4 (EPR4) are common due to their good performance on moderate density and high density channels. At higher densities, higher order polynomials such as EEPR4 have been proposed. These partial responses are of the form (1-D)(1+D).sup.n, with n determining the order of the polynomial. As n increases, the high frequency response is attenuated, hence better matching the high frequency attenuation of the magnetic recording channel at high recording densities.
As recording densities increase, the use of trellis-based coding schemes have also been proposed. These include matched spectral null coding schemes based on the matched spectral null theorem. These have been used to increase the minimum distance on the PR4 based target from 22 to 4 and have achieved efficient implementations with practical code rates of 8/10 through the use of time varying trellises.
At higher recording densities with higher order partial responses, run length constrained codes demonstrate improved distance properties. For example, the use of an EEPR4 target with a 2/3(1,7) code increases the minimum distance from 26 to 210. Codes achieving the same increase in minimum distance but without the "d=1" constraint such as maximum transition run length (MTR) codes have been proposed for the EEPR4 partial response and finite delay tree search type detectors. These run length constrained codes help simplify the target trellis by eliminating states. Even higher rate codes to achieve the same increase in minimum distance have also been proposed. These include a family of codes and the rate 8/9 code based on a time varying MTR (TMTR) constraint.
Coding to detect and eliminate certain error events on the PR4 channel was considered. The eliminated error events were the ones most likely due to noise correlation from the equalization to the PR4 response. This achieved an increase in detection SNR of .apprxeq.1.25 dB with a rate 8/9 code at recording densities around 2 bits per PW.sub.50.
A single bit parity code is utilized to detect the presence of the identified dominant error events. This coding constraint can achieve a moderate coding gain but with a high code rate which is desirable for high density magnetic recording. For the detection of the coded data, a postprocessor is possible based on correlating the received signal to identify the likely locations of the error events. The most likely event is then corrected.
The basic recording and detection system model is shown in FIG. 5 with the channel response based on the Lorentzian step response. The channel frequency response is EQU H.sub.chan (.function.)=j.pi.PW.sub.50 sin (.pi..function.T)e.sup.-.vertline..pi.PW.sup..sub.50 .function..vertline.
where PW.sub.50 is the half amplitude pulse width and T is the recorded bit period.
The recording channel is often shaped to the required target frequency response G(.function.) through the use of a continuous time and discrete time filter. For the purpose of analysis, the continuous time filter is assumed to band limit the signal and equalize it to the desired response before sampling at the baud rate 1/T. The equalizer is assumed to minimize the mean square error between the equalizer output and the desired target. This requires an equalizer response of ##EQU1##
where S.sub.x (.function.) is the power spectral density of the input data and N(.function.) is the noise power spectral density at the channel output. At the detector input, the signal consists of the input signal shaped to the desired partial response plus correlated noise with a power spectral density of ##EQU2##
While this includes distortion, it is considered as Gaussian noise for the purpose of analysis and the noise autocorrelation is assumed to be ##EQU3##
With maximum likelihood detection, the error rate performance is determined by the distance between any two allowable data sequences and the noise correlation. The probability of an error event occurring in the presence of correlated noise can be calculated as ##EQU4##
where the error event {e.sub.0,e.sub.1,. . . , ej} is the difference between any two possible noiseless sequences at the detector input and R(k) is the noise autocorrelation at the detector input. The corresponding error event in terms of channel input symbols will be denoted a.sub.k with EQU e.sub.k =a.sub.k g.sub.k
where * denotes convolution and the sequence g.sub.k is the inverse D transform of the desired target response G(D).
TABLE I RANKING OF EVENTS AT A CHANNEL DENSITY OF 3.0 BITS/PW.sub.50 Event .+-.a.sub.k SNR level (dB) +2 -2 +2 0.00 +2 -2 +2 -2 +2 0.80 +2 -2 +2 -2 +2 -2 1.35 +2 -2 +2 -2 +2 -2 +2 -2 +2 1.37 +2 -2 +2 -2 +2 -2 +2 -2 +2 -2 1.38 . . . . . .
TABLE II RANKING OF EVENTS AT A CHANNEL DENSITY OF 3.5 BITS/PW.sub.50 Event .+-.a.sub.k SNR level (dB) +2 -2 +2 0.00 +2 -2 +2 -2 +2 1.36 +2 -2 +2 -2 +2 -2 1.73 +2 -2 +2 0 0 +2 -2 +2 1.74 +2 -2 +2 -2 +2 -2 +2 -2 +2 1.89 . . . . . .
The error rate performance of the system depends on the likelihood of error events occurring and the noise correlation. As the recording density increases, the optimum target response changes and the likelihood of particular error events change relative to each other. Using the system model to calculate the noise autocorrelation and enumerating the possible error events, the relative likelihood of possible error events can be ranked. Tables I and II list the most likely error events for a channel response target of (1-D.sup.2)(2+2D+D.sup.2), taking into account noise correlation for channel recording densities of 3.0 and 3.5 bits per PW.sub.50. The tables are based on a calculated error rate of 1.times.10.sup.-6, and the likelihoods are expressed in terms of effective SNR above the most likely event. It can be seen that the events a.sub.k ={+2, -2, +2} and a.sub.k ={+2, -2, +2, -2, +2} are the most likely at these densities. If the effect of these two events can be eliminated through coding, then a coding gain can be achieved.
As the dominant error events are a.sub.k ={+2, -2, +2} and a.sub.k ={+2, -2, +2, -2, +2}, a code to detect the occurrence of these error events is required. It can readily be seen that a single bit parity check block code can be used to detect these error events. Consider a parity code of length N. Whenever one of the error events occurs within a code word, three or five bits are inverted causing a parity violation. If the error event spans the boundary of two code words, then there will be an odd number of inverted bits in one of the code words causing its parity check to be violated. Hence, the use of a single bit parity code allows the dominant error events on the high density recording channel to be detected when equalized to the proposed target response. The decoder can then pick the most likely data pattern which does not violate the parity constraint.
While an event length parity code with odd parity can provide some run length constraints with a rate (N-1)/N, stricter constraints may be required to ensure sufficient timing and gain recovery information. An interleaved run length constraint is also required to ensure Viterbi path merging on a target with a Nyquist and DC null.
While a time varying trellis incorporating the target response and the parity constraint could be constructed, it would require twice the number of states than the target response on its own. This would require a considerably more complex detector. However, decoding may be achieved through the use of a post processor. The basic detector structure is shown in FIG. 6 and is based on a Viterbi detector matched to the channel response G(D)=(1-D.sup.2)(2+2D+D.sup.2). The Viterbi outputs x.sub.k are used to reconstruct an estimate of the equalized samples y.sub.k. This is used to calculate an estimate of the noise on the equalized samples EQU n.sub.k =y.sub.k -y.sub.k.
These noise estimates are correlated with the two likely error events to produce a noise correlation for each event at each bit time. The correlation filter is the error event convolved with the channel response all reversed in time. For example, the a.sub.k ={+2, -2, +2} error event requires a correlation filter response of EQU H.sub.+2-2+2 (D)=(2-2D+2D.sup.2)G(D.sup.-1) =-2D.sup.-4 -2D.sup.-3 +2D.sup.-1 -2+4D.sup.2.
A similar filter is used for the a.sub.k ={+2, -2, +2, -2, +2} event. The noise correlation values are only considered valid if the estimated bits x.sub.k support the error event.
At each bit time the maximum of the valid noise correlation values and the corresponding type of error event is stored. At each code word boundary, the parity constraint on the estimated bits is checked. If the parity constraint is violated, the maximum valid noise correlation value over the length of the code words and across its boundaries is identified. The estimated bits x.sub.k corresponding to the error event associated with this maximum value are complemented under the assumption that the largest noise correlation value is the most likely position and error event to have occurred.
The use of such a postprocessor avoids increasing the complexity of the Viterbi detector, particularly when only a small number of error events need to be detected.
Modulation code on user data for use with recording channels is also known. Binary user data is mapped into constrained sequences, called (D,K/I) sequences, where D represents the minimum and K represents the maximum number of 0's between any pair of consecutive 1's. The parameter I represents the maximum run length of zeroes in the particular all-even and or all-odd subsequences. In a PRML system, such as EPR4, a small value of K is desirable for accurate timing and gain control, and a small value of I value reduces the length of survival registers required in the Viterbi detector due to the reducing length of the Quasi-catastrophic sequences. Using a rate 16/17 base code with constraint (0,6/8), the resulting parity code with have a 16/18 code rate. An even higher rate code can be constructed to meet run length requirements and the parity constraint. Consider a rate 16/17(0,6/8) code which consists of freely concatenateable code words of length 17. If at the end of each pair of code words (34 bits) an additional parity bit is appended, the result is a 32/35 (0,7/9) code. Likewise, if a parity bit is appended to each 3 code words (51 bits), the resulting system will attain a overall 51152 (0,7/9) code.
However, the above illustration does not take into consideration the effect of the precoder. FIG. 4A shows a system diagram with the parity bit being inserted before the write precoder, and the parity check after the postcoder during the read process. Inserting the parity bit upstream in the data before the precoder can cause considerable adverse effects. When an error occurs at the boundary of these parity-coded data blocks, the introduced parity bit cannot detect the error if the error event sequence spans over the boundaries of the parity-code data blocks. Therefore, dominant error events with long length could result in higher probability of causing a non-detectable error and reduces the effectiveness of the parity bit post-processing scheme. In an EPR4 channel, the most dominant error events are +/-(1) and +/-(1-1 1) at the output of Viterbi detector. After the postcoding, these two major errors become (1 0 1) and (1 1 0 1 1) assuming a 1/(1xor D.sup.2) precoder is being used. In both cases, length of the error events are increased by 2 bits. The invention described in this patent deals with the problems of introducing parity bit by using a write precoder with parity insertion feedback.